Aharonov-Bohm effect on the Poincaré disk

Oleg Lisovyy (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We consider formal quantum Hamiltonian of a charged particle on the Poincaré disk in the presence of an Aharonov-Bohm magnetic vortex and a uniform magnetic field. It is shown that this Hamiltonian admits a four-parameter family of self-adjoint extensions. Its resolvent and the density of states are calculated for natural values of the extension parameters.

Mots clés: Foundations of quantum mechanics; measurement theory; Integral equations

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Oleg Lisovyy. Aharonov-Bohm effect on the Poincaré disk. Journal of Mathematical Physics, 2007, 48, pp.2112. ⟨10.1063/1.2738751⟩. ⟨hal-00783926⟩